The stability of slopes has traditionally been expressed in terms of a factor of safety. Due to the uncertainties associated with the input variables, a factor of safety greater than unity is necessary to insure an acceptably low chance of failure. While the factor of safety approach has worked reasonably well in soil mechanics, the limitations of the approach have become more apparent in jointed rock masses. There is, consequently, a trend towards expressing the stability of a slope in terms of the chance, or probability, that the slope will fail. Although there are several methods of determining the probability of failure in slope stability, the only completely general method is by means of a Monte Carlo analysis. This involves defining the distribution of each input parameter, selecting a value at random from each distribution, and using the selected values to calculate the factor of safety. This process is repeated until a distribution of factors of safety sufficient to define the probability of failure has been accumulated. The large number of repeated calculations necessary in the Monte Carlo approach means that the use of a computer is imperative. A Monte Carlo overlay package of subroutines has been developed and incorporated into rock slope stability programs for the plane, step path, two block, 3-D wedge, and general slip surface failure modes. It has also been incorporated into a progressive failure analysis using a finite element formulation.
The mechanisms by which a rock slope in a jointed rock mass can fail generally depend upon the relative orientations of the slope face and the joint sets within the rock mass. By using spherical projection techniques, it is possible to determine simply and rapidly which mechanisms of failure are kinematically possible and which are kinematically impossible.
